Quantitative Aptitude Ques 1938
Question: The angles of elevation of the top of a tower from two points which are at distances of 10 m and 5 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is
Options:
A) $ 5m $
B) $ 15m $
C) $ \sqrt{50}m $
D) $ \sqrt{75}m $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given that, angles are complementary. Let h be the height of the tower. Now, in $ \Delta PBC, $ $ \tan \theta =\frac{h}{5} $ (i) and in $ \Delta PAC, $ $ \tan (90{}^\circ -\theta )=\frac{h}{10} $
$ \Rightarrow $ $ \cot \theta =\frac{h}{10} $ (ii) On multiplying Eqs. (i) and (ii), we get $ \tan \theta \cdot \cot \theta =\frac{h}{5}\times \frac{h}{10} $
$ \Rightarrow $ $ \frac{h^{2}}{50}=1 $
$ \Rightarrow $ $ h=\sqrt{50}m $
which is the required height of the tower.
BETA
